If z is a function from the real line R′ to a real Hilbert space X then the covariance function ϱ of z is defined by ϱ(t, s) ≡ (z(t), z(s)). It is proved that the function (z(·), y) is of bounded ...

For 0 < 𝛼 < 1 let 𝑉(𝛼) denote the supremum of the numbers 𝜐 such that every 𝛼-Hölder continuous function is of bounded variation on a set of Hausdorff dimension 𝜐. Kahane and Katznelson (2009) ...